In this paper, we consider the pricing of financial derivatives that involve dynamic hedging strategies and payments within the planning horizon. Equity-indexed annuities (EIAs), guaranteed investment certificates (GICs) and American and barrier options are typical examples of these products. Our exploration involves the use and comparison of alternative models that use risk measures. Although the hedging is done for each observation of the input stochastic process, the appropriate mix of risk measures and state dynamic equations helps the issuer to appropriately tailor the overall risk exercise. These different models are solved by a unified backward stochastic dynamic programming framework that we imbed with parametric techniques to shorten the running time and manage the curse of dimensionality in dynamic programming. To demonstrate the flexibility of this framework we present numerical examples featuring GICs and point-to-point EIAs. Finally, by using sampling techniques, optimal hedging strategies and specific indicators of the hedging performance, we make recommendations on how to fine tune the risk measure parameters.

中文翻译：

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使用风险度量在不完整市场中进行动态对冲

在本文中，我们考虑了在规划范围内涉及动态对冲策略和支付的金融衍生品的定价。股票指数年金 (EIA)、担保投资证书 (GIC) 以及美式期权和障碍期权是这些产品的典型例子。我们的探索涉及使用和比较使用风险度量的替代模型。尽管对输入随机过程的每次观察都进行了对冲，但风险度量和状态动态方程的适当组合有助于发行人适当地调整整体风险练习。这些不同的模型由统一的后向随机动态规划框架解决，我们嵌入了参数技术，以缩短运行时间并管理动态规划中的维数灾难。为了证明该框架的灵活性，我们提供了以 GIC 和点对点 EIA 为特征的数值示例。最后，通过使用抽样技术、最佳套期保值策略和套期保值绩效的具体指标，我们提出了如何微调风险度量参数的建议。